WASHINGTON — The Supreme Court on Tuesday appeared skeptical of the way Texas decides who must be spared the death penalty on account of intellectual disability, with several justices indicating that the state’s standards were either too strict or too arbitrary.

But there was also disagreement and confusion over precisely what the state’s standards required. A lawyer for Bobby J. Moore, a death row inmate challenging his death sentence, said the state used outdated medical standards and looked to factors rooted in stereotypes.

Scott A. Keller, the Texas solicitor general, said judges there followed the requirements of a 2002 Supreme Court decision, Atkins v. Virginia. That ruling barred the execution of the intellectually disabled but largely left it to individual states to fashion their own standards in deciding who qualifies.

It was not Texas’ goal, Mr. Keller said, “to screen out individuals and deny them relief.”

Justice Anthony M. Kennedy, who often votes with the court’s four-member liberal wing to limit the death penalty, was skeptical. “But isn’t that the effect?” he asked.

Mr. Moore has been on death row since 1980 for fatally shooting a 72-year-old Houston supermarket clerk, James McCarble, during a robbery.

Clifford M. Sloan, a lawyer for Mr. Moore, said there was no doubt that his client suffered from intellectual deficits. “It’s undisputed, for example,” Mr. Sloan said, “that at the age of 13, Mr. Moore did not understand the days of the week, the months of the year, the seasons, how to tell time, the principle that subtraction is the opposite of addition or standard units of measurement.”

The state judge who heard this and other evidence, relying on current medical standards on intellectual disability, concluded that executing Mr. Moore would violate the Eighth Amendment’s ban on cruel and unusual punishment.

But the Court of Criminal Appeals, Texas’ highest court for criminal matters, reversed that ruling, saying the judge had made a mistake in “employing the definition of intellectual disability presently used.”

Texas’ approach, Justice Sonia Sotomayor said, was partly grounded in factors drawn from the fictional character of Lennie Small, the dim, hulking farmhand in John Steinbeck’s novella “Of Mice and Men.”

Image

Bobby J. Moore has been on death row since 1980 for fatally shooting James McCarble, a 72-year-old Houston supermarket clerk, during a robbery.CreditTexas Department of Criminal Justice

In 2004, in the decision that set out the standards Texas uses, Judge Cathy Cochran of the Court of Criminal Appeals wrote that Lennie should be a legal touchstone. “Most Texas citizens might agree that Steinbeck’s Lennie should, by virtue of his lack of reasoning ability and adaptive skills, be exempt” from the death penalty, she wrote.

Justice Sotomayor said Mr. Moore was at least as intellectually disabled as Lennie. “The state had no problem in saying that Lennie, even though he could work, earn a living, plan his trying to hide the death of the rabbit he killed, that he could do all of those things, and yet he was not just mildly, but severely disabled,” she said.

Mr. Moore, by contrast, she said, “was eating out of garbage cans repeatedly and getting sick after each time he did it, but not learning from his mistakes.” His few talents, she said, did not alter the analysis.

“Why is the fact that he could mow lawns and play pool indicative of a strength that overcomes all the other deficits?” she asked.

Mr. Keller, the state’s lawyer, said that the passage in Judge Cochran’s opinion concerning Lennie was an aside with no legal force.

Justice Stephen G. Breyer said there will always be borderline cases and a degree of arbitrariness in deciding who is disabled intellectually. He said he was worried that every such dispute would end up at the Supreme Court.

“What is the court supposed to do?” he asked. “Are we supposed to have all those hearings here?”

Justice Samuel A. Alito Jr. questioned whether the Supreme Court was obliged to follow the view of medical societies in deciding who must be spared execution. Constitutional law, he said, was different from standards adopted by a majority vote of a professional organization.

The Supreme Court on Tuesday also issued its first decision in an argued case this term, ruling that a Puerto Rican politician and a business executive there must face a second trial on bribery charges. The case, Bravo-Fernandez v. United States, No. 15-537, arose from a trip to Las Vegas by the politician, Héctor Martínez-Maldonado, partly paid for by the executive, Juan Bravo-Fernandez.

A jury convicted the two men of bribery, but acquitted them of related charges that they had traveled or conspired to commit bribery. The verdicts are impossible to reconcile, both sides agreed, as the only contested issue on any of the charges was whether there had been bribery.

A federal appeals court later vacated the remaining convictions, saying that the judge had given jurors too much leeway by allowing them to convict if they found the executive had made the payments in gratitude rather than, as the law required, as part of a quid quo pro exchange.

The men had contended that the second trial violated the Constitution’s double jeopardy clause.

Justice Ruth Bader Ginsburg announced the court’s unanimous decision from the bench. Apparently suffering from a bad cold, she spoke in a halting, raspy voice, saying the case’s tangled procedural history “does not bar retrial of the defendants.”